无言证明：赫恩的余弦定律分割

GeoGebra 命令及参数

1. Circle(Q, R) → c_1
2. Intersect(xAxis, yAxis) → A
3. Point(xAxis) → C
4. Point(xAxis) → E
5. Point(xAxis) → F
6. Ray(E, F) → f
7. PointIn(c_1) → D
8. Point(f) → G
9. Polygon(D, A, G) → t1, g, d, a
10. Polygon(D, G, 4) → poly1, h, i, j, k, H, I
11. Polygon(G, A, 4) → poly2, l, m, n, p, J, K
12. Polygon(A, D, 4) → poly3, q, r, s, t, L, M
13. Midpoint(I, G) → N
14. Line(I, D) → e
15. Intersect(e, poly3) → O, P
16. Line(K, a) → f_1
17. Intersect(f_1, m) → U
18. If(0 < b < 1, Segment[D, Dilate[D, 1 - b, P]], Segment[D, P]) → g_1
19. If(2 < b < 3, Segment[K, Dilate[K, 3 - b, U]], Segment[K, U]) → h_1
20. If(2 < b < 3, Segment[G, Dilate[G, 3 - b, D]], Segment[G, D]) → i_1
21. Segment(K, U) → j_1
22. Polygon(P, L, D) → t2, d_1, p_1, l_1
23. Polygon(P, M, A, D) → q1, p_2, m_1, a_1, d_2
24. Polygon(U, J, K) → t3, k_1, u, j_2
25. Polygon(U, A, G, K) → q2, u_1, a_2, g_2, k_2
26. If(4 < b < 5, Polygon[Translate[P, Vector[D, Dilate[D, 5 - b, H]]], Translate[L, Vector[D, Dilate[D, 5 - b, H]]], Translate[D, Vector[D, Dilate[D, 5 - b, H]]]], Polygon[Translate[P, Vector[D, H]], Translate[L, Vector[D, H]], Translate[D, Vector[D, H]]]) → t4
27. If(5 < b < 6, Polygon[Translate[P, Vector[D, Dilate[D, 6 - b, I]]], Translate[M, Vector[D, Dilate[D, 6 - b, I]]], Translate[A, Vector[D, Dilate[D, 6 - b, I]]], Translate[D, Vector[D, Dilate[D, 6 - b, I]]]], Polygon[Translate[P, Vector[D, I]], Translate[M, Vector[D, I]], Translate[A, Vector[D, I]], Translate[D, Vector[D, I]]]) → q3
28. If(6 < b < 7, Polygon[Translate[U, Vector[K, Dilate[K, 7 - b, H]]], Translate[J, Vector[K, Dilate[K, 7 - b, H]]], Translate[K, Vector[K, Dilate[K, 7 - b, H]]]], Polygon[Translate[U, Vector[K, H]], Translate[J, Vector[K, H]], Translate[K, Vector[K, H]]]) → t5
29. If(7 < b < 8, Polygon[Translate[U, Vector[K, Dilate[K, 8 - b, G]]], Translate[A, Vector[K, Dilate[K, 8 - b, G]]], Translate[G, Vector[K, Dilate[K, 8 - b, G]]], Translate[K, Vector[K, Dilate[K, 8 - b, G]]]], Polygon[Translate[U, Vector[K, G]], Translate[A, Vector[K, G]], Translate[G, Vector[K, G]], Translate[K, Vector[K, G]]]) → q4
30. Translate(M, Vector[D, I]) → M'
31. Translate(P, Vector[D, I]) → P'
32. Translate(A, Vector[D, I]) → A'
33. Translate(G, Vector[K, G]) → G'
34. Translate(G, Vector[D, P']) → G'_1
35. If(9 < b < 10, Polygon[M', A', Dilate[A', 10 - b, H], Dilate[M', 10 - b, G']], Polygon[M', A', H, G']) → q5
36. Translate(U, Vector[K, H]) → U'
37. Circle(M', Segment[U', A']) → c
38. Segment(M', G') → n_1
39. Intersect(c, n_1) → S,
40. Polygon(M', S, A') → t6, a', m', s_1
41. If(11 < b < 12, Rotate[Polygon[Translate[M', Vector[M', Dilate[M', 12 - b, A']]], Translate[S, Vector[M', Dilate[M', 12 - b, A']]], Translate[A', Vector[M', Dilate[M', 12 - b, A']]]], ((b - 11) * π / 2), A'], Rotate[Polygon[Translate[M', Vector[M', A']], Translate[S, Vector[M', A']], Translate[A', Vector[M', A']]], π / 2, A']) → t7
42. Circle(H, Segment[G'_1, G']) → e_1
43. Segment(G', H) → q_1
44. Intersect(e_1, q_1) → T,
45. Polygon(A', T, H) → t8, h_2, a'_1, t_1
46. If(12 < b < 13, Rotate[Polygon[Translate[A', Vector[H, Dilate[H, 13 - b, G']]], Translate[T, Vector[H, Dilate[H, 13 - b, G']]], Translate[H, Vector[H, Dilate[H, 13 - b, G']]]], ((b - 12) * π / 2), G'], Rotate[Polygon[Translate[A', Vector[H, G']], Translate[T, Vector[H, G']], Translate[H, Vector[H, G']]], π / 2, G']) → t9
47. If(10 < b < 11, Segment[A', Dilate[A', 11 - b, S]], Segment[A', S]) → r_1
48. If(10 < b < 11, Segment[A', Dilate[A', 11 - b, T]], Segment[A', T]) → b_1
49. Polygon(S, A', T, G') → q6, s_2, a'_2, t_2, g'
50. If(13 < b < 14, Rotate[Polygon[Translate[S, Vector[T, Dilate[T, 14 - b, P']]], Translate[A', Vector[T, Dilate[T, 14 - b, P']]], Translate[T, Vector[T, Dilate[T, 14 - b, P']]], Translate[G', Vector[T, Dilate[T, 14 - b, P']]]], ((b - 13) * π / 2), P'], Rotate[Polygon[Translate[S, Vector[T, P']], Translate[A', Vector[T, P']], Translate[T, Vector[T, P']], Translate[G', Vector[T, P']]], π / 2, P']) → q7